Active Sensing of Social Networks

TL;DR

This paper introduces an active sensing approach, called social RADAR, to estimate trust levels in social networks by analyzing agents' opinions influenced by stubborn agents, framing it as a blind compressed sensing problem.

Contribution

It develops a novel active sensing method for social networks using stubborn agents to reveal network structure, with theoretical guarantees and practical estimators.

Findings

Network structure can be identified with enough stubborn agents.

Proposed estimators are consistent under deterministic and randomized models.

Simulation results validate the approach on synthetic and real networks.

Abstract

This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors' information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model under the influence of stubborn agents, i.e., agents whose opinions are not influenced by their neighbors. This method can be viewed as a \emph{social RADAR}, where the stubborn agents excite the system and the latter can be estimated through the reverberation observed from the analysis of the agents' opinions. The social network sensing problem can be interpreted as a blind compressed sensing problem with a sparse measurement matrix. We prove that the network structure will be revealed when a sufficient number of stubborn agents independently influence a number of ordinary (non-stubborn) agents. We investigate the scenario with a deterministic or randomized DeGroot model and propose a consistent estimator of the steady states for the latter scenario. Simulation results on synthetic and real world networks support our findings.